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randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has and equal chance of reaching any of the solutions of the target system T.
i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                  2                                     
o2 = ({(- .0482063 - .290609*ii)x1  + (- .136804 - .271511*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .229205 - .0571298*ii)x2  + (.00906342 - .116176*ii)x1*x3 + (- .0354071
     ------------------------------------------------------------------------
                                                    2              
     + .0543236*ii)x2*x3 + (.101409 + .0996367*ii)x3 , (- .240182 +
     ------------------------------------------------------------------------
                  3                           2                 
     .200112*ii)x1  + (.379537 - .173093*ii)x1 x2 + (- .187369 -
     ------------------------------------------------------------------------
                     2                             3               
     .218824*ii)x1*x2  + (- .284892 - .131797*ii)x2  + (- .337523 -
     ------------------------------------------------------------------------
                  2                                                  
     .181406*ii)x1 x3 + (.341096 - .192761*ii)x1*x2*x3 + (- .464961 -
     ------------------------------------------------------------------------
                  2                                2             
     .159109*ii)x2 x3 + (.340059 + .277587*ii)x1*x3  + (.735771 +
     ------------------------------------------------------------------------
                     2                             3
     .453696*ii)x2*x3  + (- .106511 - .148823*ii)x3 },
     ------------------------------------------------------------------------
     {{-.0704939+.231029*ii, .68005+.231062*ii, .651768+.031582*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{{.031462-.463469*ii, .613038+.336747*ii, .47214+.26847*ii}, #steps =>
     ------------------------------------------------------------------------
     12, status  => REGULAR, last t => 1, cond#^{-1} => .439302}}

o3 : List

Ways to use randomInitialPair :